Non-simplifying Graph Rewriting Termination

TL;DR

This paper explores the termination properties of graph rewriting systems in NLP, showing that while uniform termination is undecidable, non-uniform termination is decidable, and introduces techniques for analyzing termination.

Contribution

It demonstrates the undecidability of uniform termination and provides methods for deciding non-uniform termination in graph rewriting systems used in NLP.

Findings

Uniform termination is undecidable.

Non-uniform termination is decidable.

Two termination techniques based on weights are proposed.

Abstract

So far, a very large amount of work in Natural Language Processing (NLP) rely on trees as the core mathematical structure to represent linguistic informations (e.g. in Chomsky's work). However, some linguistic phenomena do not cope properly with trees. In a former paper, we showed the benefit of encoding linguistic structures by graphs and of using graph rewriting rules to compute on those structures. Justified by some linguistic considerations, graph rewriting is characterized by two features: first, there is no node creation along computations and second, there are non-local edge modifications. Under these hypotheses, we show that uniform termination is undecidable and that non-uniform termination is decidable. We describe two termination techniques based on weights and we give complexity bound on the derivation length for these rewriting system.